Chaotic electron trajectories in a free-electron laser with helical wiggler and ion-channel guiding

Abstract

An analysis of relativistic electron trajectories in a free-electron laser with a helical magnetic wiggler and an ion channel is presented. The wiggler field amplitude and the ion number density are taken to be uniform. Also included are the self-electric and self-magnetic fields of the electron beam, which is assumed to be of constant velocity and electron number density. The Hamiltonian, which is a constant of the motion, is first expressed in cartesian coordinates and momenta. A second constant of the motion is obtained by canonical transformation. The steadystate orbits, Poincare maps, and Liapunov exponents are employed to investigate the chaotic motion in the presence of the ion channel. Numerical calculations reveal conditions under which chaotic and non-chaotic orbits exist.